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Electrostatic solution of massless quenches in Luttinger liquids
by Paola Ruggiero, Pasquale Calabrese, Thierry Giamarchi, Laura Foini
|As Contributors:||Thierry Giamarchi · Paola Ruggiero|
|Arxiv Link:||https://arxiv.org/abs/2203.06740v3 (pdf)|
|Date submitted:||2022-05-22 18:54|
|Submitted by:||Ruggiero, Paola|
|Submitted to:||SciPost Physics|
The study of non-equilibrium dynamics of many-body systems after a quantum quench received a considerable boost and a deep theoretical understanding from the path integral formulation in imaginary time. However, the celebrated problem of a quench in the Luttinger parameter of a one dimensional quantum critical system (massless quench) has so far only been solved in the real-time Heisenberg picture. In order to bridge this theoretical gap and to understand on the same ground massive and massless quenches, we study the problem of a gaussian field characterized by a coupling parameter K within a strip and a different one K0 in the remaining two semi-infinite planes. We give a fully analytical solution using the electrostatic analogy with the problem of a dielectric material within a strip surrounded by an infinite medium of different dielectric constant, and exploiting the method of charge images. After analytic continuation, this solution allows us to obtain all the correlation functions after the quench within a path integral approach in imaginary time, thus recovering and generalizing the results in real time. Furthermore, this imaginary-time approach establishes a remarkable connection between the quench and the famous problem of the conductivity of a Tomonaga-Luttinger liquid coupled to two semi-infinite leads: the two are in fact related by a rotation of the spacetime coordinates.
Author comments upon resubmission
We are submitting a revised version of the manuscript
“Electrostatic solution of massless quenches in Luttinger liquids”.
We would like to thank the editors for their work and the referees for
their useful comments and suggestions.
We believe that we thoroughly addressed all the comments of the referees
in the new version of the manuscript.
List of changes
- Few typos corrected
- New section added (Section 7)
- Last sentence in Appendix added
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2022-6-5 (Invited Report)
I thank the authors for their reply to my questions about the manuscript. As stated in my previous report, the manuscript is scientifically correct and well-written. It elaborates on the study of the massless quench in Luttinger liquids, which has a broad interest for the community working on the non-equilibuim dynamics after a quench. On a more technical side, it gives an exact analytic solution for the Green's function in an inhomogeneous medium. Despite the simple form of the inhomogeneity of the Luttinger parameter, this result is quite remarkable. For these reasons, I recommend this manuscript for the publication in SciPost Physics.
Anonymous Report 1 on 2022-5-27 (Invited Report)
I thank the authors for their detailed response. Unfortunately they appear to have misunderstood my main point, which was not that the whole approach using imaginary time is narrow and pedestrian, but that this particular contribution, although correct, is so, and is not at the level suitable for publication in SciPost.